Bard College
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Senior Projects Spring 2013 Bard Undergraduate Senior Projects
2013
Recreating the Trajectory of a Golf Swing Using a
Microelectromechanical System
Blagoy Yordanov Kaloferov
Bard College
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Recommended Citation
Kaloferov, Blagoy Yordanov, "Recreating the Trajectory of a Golf Swing Using a Microelectromechanical System" (2013). Senior
Projects Spring 2013. Paper 48.
hp://digitalcommons.bard.edu/senproj_s2013/48
Recreating the Trajectory of a Golf Swing
Using a Microelectromechanical System
A Senior Project submitted to
The Division of Science, Mathematics, and Computing
of
Bard College
by
Blagoy Kaloferov
Annandale-on-Hudson, New York
May, 2013
Abstract
In the game of golf, practicing and improving the swing is a fundamental part of learning.
Unfortunately, analyzing one’s swing and all of its features is a costly and difficult task as
it involves high speed cameras or the assistance of a coach. This paper presents a novel
approach to golf swing analysis using a microelectromechanical system containing sensors
that are attached to a golf club. This novel hardware system has been constructed using
commercially available components. A displacement estimation algorithm compensates for
the errors of the MEMS sensors. The raw data from the sensors is processed using a sensor
fusion orientation estimation algorithm and the displacement estimation algorithm. Finally
an application has been developed to help visualize the trajectory of the golf swing and
give feedback on the swing’s key features. The hardware prototype built for the purpose
has 9 degrees of freedom, communicates wirelessly and has expandable storage. Because
it is both an attitude and heading reference system and an inertial measurement unit its
use could be extended to other sports or applications.
Contents
Abstract 1
Dedication 7
Acknowledgments 8
1 Introduction 9
2 MEMS Sensors and Prototype Hardware Configuration 12
2.1 Accelerometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Mechanical Accelerometer . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.2 MEMS Accelerometer . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.3 MEMS Accelerometer Error Sources . . . . . . . . . . . . . . . . . . 14
2.1.4 Accelerometer ADXL345 . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Gyroscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1 MEMS Gyroscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 MEMS Gyroscope Sources of Error . . . . . . . . . . . . . . . . . . . 16
2.2.3 Gyroscope ITG3200 . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Magnetometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.1 Magnetometer sources of error . . . . . . . . . . . . . . . . . . . . . 17
2.4 Magnetometer HMC5883L . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Wireless Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6 Data Logging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.6.1 SD Card Storage Expansion . . . . . . . . . . . . . . . . . . . . . . . 18
2.7 Microcontroller Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.7.1 Arduino electronics and programing platform . . . . . . . . . . . . . 19
2.7.2 Teensy 3.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Contents 3
2.8 9 Degrees of Freedom Sensor Stick . . . . . . . . . . . . . . . . . . . . . . . 20
2.9 Final Prototype Configuration . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.9.1 Hardware configuration . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 Orientation and Displacement Estimation of a Rigid Object 26
3.1 Quaternion representation of the orientation of a rigid body . . . . . . . . . 26
3.2 Orientation Representation Using Sensor Fusion . . . . . . . . . . . . . . . . 28
3.2.1 Orientation from Angular Rate Represented using Quaternion . . . . 28
3.2.2 MARG Sensor Fusion algorithm . . . . . . . . . . . . . . . . . . . . 30
3.2.3 Algorithm step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.4 Magnetic distortion compensation . . . . . . . . . . . . . . . . . . . 32
3.2.5 Algorithm pseudo code . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Position Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.1 Gravity Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.2 Displacement Estimation . . . . . . . . . . . . . . . . . . . . . . . . 36
4 Golf terminology and GolfSwing Application 38
4.1 Golf Swing phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.1.1 Follow-through phase . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2 GolfSwing Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2.1 Processing Application Overview . . . . . . . . . . . . . . . . . . . . 41
4.2.2 Feedback on a golf swing . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3 IMU System Data Recording Process Overview . . . . . . . . . . . . . . . . 43
5 Sensor Performance Optimization and Data Processing Algorithm 45
5.1 Orientation and displacement estimation without filters . . . . . . . . . . . 45
5.1.1 Orientation estimation without filtering . . . . . . . . . . . . . . . . 46
5.1.2 Position estimation without filtering . . . . . . . . . . . . . . . . . . 49
5.2 Displacement estimation optimization . . . . . . . . . . . . . . . . . . . . . 51
5.3 IMU Placement on a Golf Club . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.3.1 IMU at the head of the club . . . . . . . . . . . . . . . . . . . . . . 53
5.3.2 IMU at the grip of a club . . . . . . . . . . . . . . . . . . . . . . . . 53
5.4 Final Displacement and Orientation Estimation Processing Algorithm . . . 53
6 IMU Prototype Evaluation with Simulations 55
6.1 Process of Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.2 Golf Swing simulation using Pendulum . . . . . . . . . . . . . . . . . . . . . 55
6.2.1 Nonlinear Driven Damped Pendulum . . . . . . . . . . . . . . . . . . 56
6.3 Simulation Pendulum Environment . . . . . . . . . . . . . . . . . . . . . . . 57
6.4 Experiment’s Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.5.1 Position estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.5.2 Other evaluation aspects . . . . . . . . . . . . . . . . . . . . . . . . . 65
7 Conclusion and Future Work 67
Contents 4
Bibliography 69
List of Figures
2.1.1 Basic spring-mass system accelerometer . . . . . . . . . . . . . . . . . . . . 13
2.1.2 The core micromechanical structure of a 3-axis MEMS accelerometer . . . . 14
2.7.1 Arduino Uno, AA battery and Teensy 3.0 size comparison . . . . . . . . . . 20
2.8.1 Sensor Stick sold by SparkFun. . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.9.1 All major components of the IMU prototype . . . . . . . . . . . . . . . . . 23
2.9.2 Top View of the device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.9.3 IMU with closed enclosure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.9.4 The back of the IMU main board without the modules . . . . . . . . . . . . 25
2.9.5 The front of the IMU main board without the modules . . . . . . . . . . . . 25
4.1.1 The path of a golf club during a typical full golf swing . . . . . . . . . . . . 38
4.1.2 Composition of a golf club . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.1.3 Possible paths of the clubhead during the follow-through phase of a golf
swing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2.1 GolfSwing application and its menu. . . . . . . . . . . . . . . . . . . . . . . 42
5.1.1 Determining the orientation of the device and displaying it using Processing 46
5.1.2 Yaw Pitch Roll estimations when IMU is placed stationary . . . . . . . . . 47
5.1.3 Actuator setup used to rotate the IMU . . . . . . . . . . . . . . . . . . . . . 48
5.1.4 Euler angles estimation during actuator rotation . . . . . . . . . . . . . . . 49
5.1.5 IMU’s displacement over time without any filtering . . . . . . . . . . . . . . 50
5.2.1 IMU’s displacement over time with filtering . . . . . . . . . . . . . . . . . . 52
6.3.1 Pendulum equipment designed to simulate a simple golf swing . . . . . . . . 58
6.4.1 Histogram of the X axis accuracy for 40 golf swing simulations. . . . . . . . 59
6.4.2 Histogram of the Y axis accuracy for 40 golf swing simulations . . . . . . . 59
6.4.3 Histogram of the Z axis accuracy for 40 golf swing simulations . . . . . . . 60
LIST OF FIGURES 6
6.4.4 Histogram of the accuracy of all axes for 40 golf swing simulations . . . . . 60
6.4.5 The accuracy for 40 golf swing simulations for 0.93 seconds. . . . . . . . . . 61
6.4.6 The path of a pendulum rod the club head path estimated using the pen-
dulum experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.4.7 The path of the clubhead and the end of the pendulum rod of a simulation 63
6.4.8 The expected path of rod end over 5 seconds on the pendulum . . . . . . . 64
Dedication
To my family for their love and support.
Acknowledgments
First of all, I would like to thank my advisor Rebecca Thomas for giving me the right
directions when necessary, but also letting me explore on my own, all possible choices
regarding this project. That gave me a perfect balance of learning new things, and pro-
gressing adequately with the project, throughout the past year.
BIG thanks goes to my family for always being there for me and guiding me through
times of difficult choices. I thank my girlfriend Angela, for always supporting me and mo-
tivating me to work hard and be passionate for the things that I do.
Thanks to Seth Tuckerman for helping me come up with the idea for this project, and
showing me how my work could be relevant to a golf player.
Finally thanks to my friends at the computer science department Anis Zaman and Nabil
Hossain, without whom my experience at Bard would not have been the same.
1
Introduction
More than 29 million people in the USA play golf, which involves the use of clubs to hit a
small ball into series of holes. For a successful golf game, huge importance is placed on the
golf swing. While there is sufficient literature written on the subject, an amateur golfer
would benefit enormously from having instant feedback on his or her swing. A beginner
golfer would like to recognize his or her mistakes and try to correct them. Usually there
are two options for that purpose: a coach can look at the club during a golf swing and
use accumulated experience to judge how good it is. Alternatively, a high speed camera
could record a video of the swing. Both options could be very useful, but come at a high
price. The high-speed camera requires calibration and is very expensive, not quite fitting
the role of a device that one could set up and use anywhere. Having an instructor assist a
learning golfer is viable, but does not promise technical accuracy and is often economically
unjustified for the average golfer. This senior project aims at the development of hardware
and software that could achieve a good balance between these properties: easy set up,
practical functionality, accurate feedback and low price.
1. INTRODUCTION 10
The device I designed has an accelerometer, a gyroscope and a magnetometer as sensors
attached on a common board. An accelerometer measures the gravitational force and can
be found in almost every modern smartphone. A gyroscope measures rotational velocity
and a magnetometer measures the strength of earths’ magnetic fields. The device also has a
microcontroller that controls and utilizes the sensors. The system is powered by a battery
and has sufficient memory to store a day’s worth of swings. A microelectromechanical
accelerometer, gyroscope and magnetometer are used to acquire raw data that is filtered
and processed to obtain the displacement and orientation of a golf clubhead during a golf
swing. The prototype system build for this project has 9 degrees of freedom, expandable
storage capacity and Bluetooth module. The final device has to be physically attached to
the club.
Some of the main challenges to this project come from the nature of the sensors. Since
they are not military grade sensors, they are prone to small errors that could alter the
output of the processing algorithms. During a golf swing, the rotational velocity of the golf
club could reach 1500 degrees per second and the g force that the clubhead experiences
can be as high as 16g. The time frame between the beginning of the down-swing motion
and the impact of the ball is roughly
1
3
of a second, which implies the need for a very high
sensor sampling rate and impeccable accuracy. [9] The device’s performance, as shown in
this paper, demonstrates that although constructed using cheap commercial components,
it can serve as a reliable inertial measurement unit (IMU) and attitude and heading
reference system (AHRS). This paper proposes a methodology for capturing and analyzing
the following features of a golf swing: the golf club’s trajectory, velocity and its orientation
throughout the golf swing. In addition to that, we are proposing a software application
that interfaces the prototype system.
The rest of the paper is organized as follows. Chapter 2 provides an introduction to all
components chosen for the system. It also gives an overview of the design of the hardware
1. INTRODUCTION 11
prototype that was built. Chapter 3 explains the theory behind the algorithm employed for
orientation sensing and gravity compensation and how displacement should be calculated
to minimize errors. Chapter 4 explains which features of a golf swing can be captured by
the proposed device and how they are relevant to a golfer. It also examines an application,
designed to facilitate the hardware system, attached to a golf club. Chapter 5 provides
techniques for optimizing the performance of the system and an empirical evaluation of
the efficiency of these techniques. Chapter 6 presents a golf swing simulation equipment,
used to evaluate the performance of the device and its processing algorithms. The paper
closes with conclusion and future work suggestions in Chapter 7.
2
MEMS Sensors and Prototype Hardware
Configuration
Microelectromechanical sensors are miniature devices that convert a non-electrical quan-
tity into an electrical signal. By integrating a micro sensor with a microprocessor, a smart
sensor called a microelectromechanical system (MEMS) is produced. MEMS systems con-
tain electrical and mechanical parts. [8] Accelerometers, gyroscopes and magnetometers
are MEMS sensors that the prototype system described in this paper incorporates. They
convert energy from one form to another, thus generating output. When aligned together
on a common board the sensors can be used to perform complicated tasks. Having the
sensors aligned means that their x, y and z axis are parallel to each other. The prototype
system also includes other components, forming an inertial measurement unit (IMU) which
is composed of sensors capable of measuring proper acceleration and angular velocity. For
simplicity, this paper will refer to the prototype system described below simply as an IMU.
It is difficult to find commercially available hardware products that are portable, act as
an IMU and store and transfer data wirelessly. Thus, from the beginning of this project,
I was motivated by the idea of designing a device that could be assembled using only
components that are easily available on the electronics market. For such an IMU con-
2. MEMS SENSORS AND PROTOTYPE HARDWARE CONFIGURATION 13
figuration the following constraints need to be considered: price, portability, convenient
power source, storage capacity, durability and accuracy. This chapter provides a descrip-
tion of the mechanics of the MEMS sensors chosen for the project and the other pieces of
hardware that make the prototype work as desired.
2.1 Accelerometer
2.1.1 Mechanical Accelerometer
An accelerometer is a device that will measure acceleration forces. These forces may be
static, like the force of gravity, or they could be dynamic, caused by moving or vibrating
the accelerometer. A completely stationary accelerometer on the earth’s surface would
measure a force of 1g. If an accelerometer is stationary in space it will have output of
0g in each of its axes. One can think of accelerometers as systems that have a mass
attached to a spring. Figure 2.1.1. shows how a basic, one-axis accelerometer is modeled.
Using Newton’s law, F = m ∗ A, where m is the mass and A is the acceleration, one can
calculate the acceleration of the sensor.
Figure 2.1.1: Basic spring-mass system accelerometer
[21]
2.1.2 MEMS Accelerometer
A MEMS accelerometer has many advantages compared to mechanical accelerometers.
These advantages include low cost, better performance, compactness, and multi axis sens-
2. MEMS SENSORS AND PROTOTYPE HARDWARE CONFIGURATION 14
ing on a silicon structure. MEMS accelerometers are made of a micro machined structure
that is mounted on a silicon base. It has a spring with mass-displacer that can translate
external forces such gravity into kinetic motion energy. (figure 2.1.2) As that mass expe-
riences external forces due to gravity or displacement the capacitor sensors that surround
the mass reflect those forces by outputting a change of voltage. [4] Low cost MEMS ac-
celerometers are used in many devices nowadays and are therefore cheap. They are used
for orientation sensing in smartphones, free fall detection and even impact detection in
automobile airbags.
Figure 2.1.2: The core micromechanical structure of a 3-axis MEMS accelerometer
[7]
2.1.3 MEMS Accelerometer Error Sources
MEMS accelerometers have lower power consumption and faster start-up times compared
to mechanical accelerometers. However, the sensors show some errors in their measure-
ments including dynamic error, such as measurement noise, and static errors, such as the
offset difference between the acceleration measured by the accelerometer and the actual
acceleration. Temperature changes can disturb accelerometer output too. [32]
2. MEMS SENSORS AND PROTOTYPE HARDWARE CONFIGURATION 15
2.1.4 Accelerometer ADXL345
For this project I chose to use accelerometer ADXL345 manufactured by Analog Devices.
The ADXL345 is a small, thin, low-power, 3-axis accelerometer with high resolution (13-
bit) measurement at up to 16 g. Digital output data is accessible through I
2
C digital
interface. I
2
C is a two wire interface allowing for communication between a microcontroller
and peripheral device. In addition to that this model has been used in a variety of devices
and due to the high volumes in production it is relatively cheap. [1]
2.2 Gyroscope
A gyroscope is a device that is used for orientation sensing based on angular momentum.
In its basic mechanical form it is a spinning wheel that is free to assume any orientation.
The wheel is attached on two gimbals and since it is rotating rapidly, its momentum keeps
its orientation fixed when the gimbals’ orientations are changed. The gyroscope measures
the angle between the adjacent gimbals to estimate orientation. [32] Mechanical gyroscopes
are accurate, but are expensive, require moving parts and cannot be constructed on micro
scale.
2.2.1 MEMS Gyroscope
MEMS gyroscopes are made with the use of silicon micro-machining techniques. They are
small and can be very inexpensive since MEMS gyroscopes are widely used in smartphones
and game controllers. MEMS gyroscopes contain a vibrating structure that because of its
vibration remains unaffected by the orientation change of its support. MEMS gyroscopes
are excellent candidates for the data recording device of this project as they have small
weight and size, low price and low power consumption.
2. MEMS SENSORS AND PROTOTYPE HARDWARE CONFIGURATION 16
2.2.2 MEMS Gyroscope Sources of Error
MEMS gyroscopes’ output is prone to errors that we must note as they are of importance in
this paper. A constant bias error is the average output of a gyro, when it is not undergoing
any rotation. Offset error is the difference between the output of the gyro and its true value.
The output of gyroscopes is also negatively affected by mechanical noise, which fluctuates
at a rate much greater than the sampling rate of the actual sensor. Finally temperature
changes in the sensor fluctuate its output. [32]
2.2.3 Gyroscope ITG3200
MEMS gyroscope ITG-3200 is a 3-axis gyroscope produced by Invensense. The chip sup-
ports Fast-Mode I
2
C (400 kHz) interface and has an embedded temperature sensor. It can
detect angular change of up to 2000 degrees per second which makes it capable of accu-
rately recording golf swings that have fast rotational velocity of 1500 degrees per second.
[14]
2.3 Magnetometer
A Magnetometer is a type of sensor that measures the strength and direction of its local
magnetic field. The magnetic field measured will be a combination of the earth’s magnetic
field and any magnetic field created by nearby objects. [29] The Earth generates a magnetic
field that creates measurable magnetic disturbances in the atmosphere. A magnetometer
measures this phenomenon in terms of magnetic flux density. That magnetic flux can be
treated as a vector that has direction and magnitude. [6] A magnetometer is an ideal
supplement to an inertial measurement unit, because it is inexpensive and has low power
consumption.
2. MEMS SENSORS AND PROTOTYPE HARDWARE CONFIGURATION 17
2.3.1 Magnetometer sources of error
Magnetometers are not perfect because their output is distorted by other magnetic fields,
including the magnetic fields created by components near the magnetometer. If mag-
netometers were completely reliable, we would not need gyroscopes and accelerometers.
Magnetometer readings need to be filtered and corrected because of any distortion that
they are subject to. [15] An orientation estimation sensor fusion algorithm presented in
section 3.2.2 elaborates on such adjustment technique.
2.4 Magnetometer HMC5883L
I chose to use MEMS magnetometer HMC5883L produced by Honeywell. The Honeywell
HMC5883L is a surface-mount, multi-chip module designed for low-field magnetic sensing
with I
2
C digital interface for applications such as low-cost compassing and magnetometry.
The HMC5883L can produce 12-bit output at rate of 160 Hz. The sensor is popular for
electronics prototyping and therefore has good online community support. [13]
2.5 Wireless Communication
For wireless communication, I was faced with the choice of using a low power radio chip,
a Bluetooth module or a Wi-Fi chip. A radio chip has very low power consumption, which
is good for a battery-powered device, but it is also limited by the fact that it can only
communicate with another radio chip that has the same frequency. That makes pairing
the system with smartphones or computers difficult. A Wi-Fi module has the best speed
and range but its high battery consumption could negatively affect the performance of the
IMU. Bluetooth chips contain the best balance between speed, communication range and
battery consumption and most of all, almost all modern mobile devices and computers are
Bluetooth enabled. The chip I chose is the Bluetooth Silver Mate, produced and sold by
2. MEMS SENSORS AND PROTOTYPE HARDWARE CONFIGURATION 18
Sparkfun Electronics. It has FCC Approved Class 2 Bluetooth radio modem that supports
serial speed of up to 115200 bps.
2.6 Data Logging
2.6.1 SD Card Storage Expansion
The storage capacity of the microcontroller, used for the IMU device is insufficient to
store more than few seconds of data, due to its limited memory capacity. (table 2.7.1)
Therefore, some additional storage space for data logging was essential to the success of
the project. I decided to use a SD card adaptor that would enable me to store a practically
unlimited amount of data. The drivers for the adapter are incorporated in microcontroller
library called SDFat. SDFat is an Arduino library that supports FAT16 and FAT32 file
systems on standard and high capacity SD cards. [25] I created custom code that would
save the data according to my needs. A Micro SD card of 4 GB, for example, not only
makes data logging possible, but is also convenient as it allows an alternative data transfer
to a computer.
2.7 Microcontroller Unit
A microcontroller is necessary to integrate all components of the IMU system and to
facilitate communication with a computer. A microcontroller is a small computer with
integrated processor, memory and input/output peripherals. I decided to work with the
Arduino electronics platform and after comparing microcontrollers, I chose a chip that is
Arduino compatible but manufactured by a different company, due to its better charac-
teristics.
2. MEMS SENSORS AND PROTOTYPE HARDWARE CONFIGURATION 19
2.7.1 Arduino electronics and programing platform
Arduino is an open-source electronics prototyping platform based on flexible, easy-to-use
hardware and software. [2] It is an excellent choice as a microcontroller platform because it
has a functional and easy to use IDE, excellent support community and low price. There are
various libraries written to support additional components that Arduino microcontrollers
can utilize. Some of these components include motors, Wi-Fi, Ethernet shields and even
touch-screens. Most of all, there are drivers for dozens of MEMS sensors that were written
for Arduino. Initially, I chose to use the most popular Arduino board to date: Arduino
UNO. Arduino UNO has all the standard capabilities in the Arduino microcontrollers
family and has a good balance between functionality and size. Its price is $35. Eventually
I replaced Arduino UNO with a more suitable microcontroller called Teensy 3.0.
2.7.2 Teensy 3.0
Midway through my senior project at the end of November 2012 a 32-bit microcontroller
called Teensy 3.0 was commercially released at the very low price of $19. It is produced
by a small company called PJRC and is now the default choice for many people working
on electronics projects because of its specifications. In addition, it is compatible with the
Arduino IDE. Teensy is faster, smaller and has better technical specifications as shown in
table 2.7.1. [28]
Specifications Arduino Uno Teensy 3.0
Processor Atmega328 16 MHz MK20DX128 32-bit ARM 48 MHz
RAM Memory 2 KB 16 KB
Flash Memory 32 KB 130 KB
Serial, I
2
C, SPI 1, 1, 1 3, 1 ,1
EEPROM 1 KB 2 KB
I/O 14 / 5V 34 / 3.3V
Price $35 $19
Table 2.7.1: Arduino UNO and Teensy 3.0 technical specifications
2. MEMS SENSORS AND PROTOTYPE HARDWARE CONFIGURATION 20
Some mathematical operations have to be performed on the microcontroller for this
project as shown in Chapter 4. Therefore, more RAM and clock speed that is 3 times that
of Arduino UNO are important for increasing the sample rate of the IMU system. As a
result, I chose to use Teensy 3.0 as the microcontroller for final IMU design and evaluation.
Figure 2.7.1: Arduino Uno, AA battery and Teensy 3.0 size comparison
Figure 2.7.1 shows Teensy’s size relative to a Arduino UNO and an AA battery. Teensy
3.0 has the size of one of the most miniature microcontrollers used for electronics prototyp-
ing and also has the power and functionality of some of the most expensive microcontrollers
on the market up to date. However, I had to optimize all the drivers for the sensors I have
chosen due to the drivers’ incompatibility with 32-bit microcontrollers. In the rest of the
paper, any reference to Arduino compatible code implies that the code is compatible with
Teensy 3.0 unless specifically noted otherwise.
2.8 9 Degrees of Freedom Sensor Stick
The three MEMS sensors that I chose to use are incorporated on the same board and
sold by SparkFun Electronics. The board is called Sensor Stick and its combination of
2. MEMS SENSORS AND PROTOTYPE HARDWARE CONFIGURATION 21
sensors gives it 9 degrees of freedom. It includes ADXL345 accelerometer, HMC5883L
magnetometer, and ITG-3200 gyroscope as introduced earlier in this chapter. The board
has I
2
C interface and is very small, measuring just 34x10 mm. (figure 2.8.1)
Figure 2.8.1: Sensor Stick sold by SparkFun.
[26]
2.9 Final Prototype Configuration
This section provides an overview of the design of the prototype system, which is physically
attached to a golf club and has all components described in this chapter.
2.9.1 Hardware configuration
The final IMU system has a main board that connects and powers all of its elements.
Figure 2.9.5 shows the board’s layout. In order to make the device adaptive, I avoided
soldering components directly to the main board. That is important for a prototype system
because its elements can be treated as modules and replaced. The board can be placed in
a protective enclosure. The system could be even smaller, should all elements be soldered
directly onto a main board or should one choose to use Printed Circuit Board software to
design a platform containing all components. These options are beyond the scope of this
project but we have provided a list of all elements for such purposes. Figure 2.9.1 provides
2. MEMS SENSORS AND PROTOTYPE HARDWARE CONFIGURATION 22
a picture of all individual elements together. They can be easily purchased from any major
online retailer like SparkFun Electronics. The list of the components is as follows:
1. Teensy 3.0 - The main microcontroller unit. It powers and controls all components.
2. Sensor Stick - The sensors board. Having accelerometer, gyroscope and magne-
tometer means that the sensor board gives the device 9 degrees of freedom. It con-
nects to Teensy 3.0 using I
2
C interface.
3. Micro SD card adapter - When combined with an MicroSD card the adapter will
enable storage expansion. That is important because the data cannot be stored in
the microcontroller.
4. Bluetooth Mate Silver - The module enables wireless communication with com-
puters or tablets. It is connected to the microcontroller using a serial port.
5. Meas Vibration Sensor - A vibration sensor (not shown in figure 2.9.1) capable
of detecting actions ranging from a single tap to the impact between a golf club and
a golf ball.
6. 3.7V 850 mA Battery - This small, light battery can power the device for more
than 2 hours.
7. PCB Case - The protective enclosure of the main board that protects all compo-
nents. It measures 101x50x25 mm and can be opened for easy access to the prototype
elements
2. MEMS SENSORS AND PROTOTYPE HARDWARE CONFIGURATION 23
Figure 2.9.1: All major components of the IMU prototype
The IMU can be powered both using its USB connector or a battery and can be con-
trolled over Bluetooth. Sensors communicate with the microcontroller Teensy 3.0 using
I
2
C bus interface. Additionally, Teensy 3.0 supports up to three hardware serial port con-
nections. We are utilizing one of them for connection with the Bluetooth module which
in turn communicates with a receiving computer. Finally, a direct physical connection
between Teensy 3.0 and a computer can be established using the microcontroller’s built
in micro USB port. Figure 2.9.3 shows the assembled device with its enclosure.
Table 2.9.2 shows the price of all components of the hardware configuration. With a
total cost of less than $200, the IMU system is cheap considering its multiple features.
Furthermore, there are very limited choices when it comes to commercial small MEMS
inertial measurement units. Section 6.5.2 provides a comparison between the prototype
device and similar commercial product.
2. MEMS SENSORS AND PROTOTYPE HARDWARE CONFIGURATION 24
Degrees of Freedom 9 DOF
Features Vibration Sensor, SD card storage expansion
Communication USB , Bluetooth
Accelerometer 16g
Gyroscope 2000 deg/sec
Size 101x50x25 mm
Sample Rate 400 Hz
Table 2.9.1: Technical specifications of the IMU system
Component Price
Teensy 3.0 $19
9 DOF Sensor Stick $99
Bluetooth Mate $39
SD Card Adapter $7
850 mA Battery $10
Meas Vibration Sensor $3
PCB Enclosure $5
Other Components $15
Total Cost $197
Table 2.9.2: Price of the components of the IMU system
Figure 2.9.2: Top View of the device
Figure 2.9.3: IMU with closed enclosure
2. MEMS SENSORS AND PROTOTYPE HARDWARE CONFIGURATION 25
Figure 2.9.4: The back of the IMU main board without the modules
Figure 2.9.5: The front of the IMU main board without the modules
3
Orientation and Displacement Estimation of a
Rigid Object
This chapter provides an introduction to orientation sensing using MEMS sensors. Quater-
nions, which are used to represent orientation are defined and introduced. A magnetic,
angular rate, gravity (MARG) sensor fusion algorithm that can utilize a 9 degrees of
freedom sensor board is presented. I have adapted this algorithm for the orientation esti-
mation of the IMU device, necessary to determine the clubhead orientation at the moment
of impact with a golf ball. The chapter also explains how an object’s displacement over
time can be calculated using an accelerometer and why the accelerometer’s output must
be compensated for the earth’s gravity.
3.1 Quaternion representation of the orientation of a rigid body
The orientation of a rigid body in three-dimensional space can be represented and stored
using quaternions. A quaternion is a four-dimensional complex number that can be treated
as a four-dimensional vector, where the last three components represent a direction vector
and the first component stands for rotation around that vector.
3. ORIENTATION AND DISPLACEMENT ESTIMATION OF A RIGID OBJECT 27
Quaternions are like extended complex numbers, w + ix + jy + kz, where i
2
= j
2
=
k
2
= −1. This section depicts important properties of quaternions deployed in this chapter
in an orientation estimation algorithm. A quaternion
A
B
ˆq represents an orientation of frame
B relative to frame A that is achieved through the rotation of angle θ around the the x,
y and z axis defined in frame A. Equation 3.1.1 shows how quaternion
A
B
ˆq is defined using
unit vector
A
ˆr in the x , y and z axes of frame A respectively. [20]
A
B
ˆq = [q
1
q
2
q
3
q
4
] = [cos
θ
2
− r
x
sin
θ
2
− r
y
sin
θ
2
− r
z
sin
θ
2
] (3.1.1)
where r
x
, r
y
and r
z
are the components of the vector
A
ˆr.
Relative frames described by an orientation can be swapped using a quaternion con-
jugate that is denoted by ∗ . Equation 3.1.2 shows how the conjugate of a quaternion is
obtained. The conjugate of a quaternion
A
B
ˆq could be thought of as
B
A
ˆq as these quaternions
describe frame B relative to frame A and frame A relative to frame B respectively.
A
B
ˆ
q∗ =
B
A
ˆq = [q
1
− q
2
− q
3
− q
4
] (3.1.2)
Quaternion product denoted by ⊗, can be used to obtain the compound orientation
of two quaternions. (equation 3.1.3). For two quaternions
A
B
ˆq and
B
C
ˆq their compound
orientation would be
A
C
ˆq.
A
C
ˆq =
B
C
ˆq ⊗
A
B
ˆq (3.1.3)
The product of two quaternions a and b is defined by the Hamilton rule [20] as shown
in equation 3.1.4. A quaternion product is not commutative.
a ⊗b = [a
1
a
2
a
3
a
4
] ⊗[b
1
b
2
b
3
b
4
] (3.1.4)
=
a
1
b
1
− a
2
b
2
− a
3
b
3
− a
4
b
4
a
1
b
2
+ a
2
b
1
+ a
3
b
4
− a
4
b
3
a
1
b
3
− a
2
b
3
+ a
3
b
1
+ a
4
b
2
a
1
b
4
+ a
2
b
3
− a
3
b
2
+ a
4
b
1
(3.1.5)
3. ORIENTATION AND DISPLACEMENT ESTIMATION OF A RIGID OBJECT 28
Quaternions can be used to rotate vectors in 3-dimensional space. Using equation 3.1.6
[17]
A
v and
B
v would be the same vectors in sensor frame A and rotated in sensor frame
B respectively. The vectors would have to be 4-dimensional with a first element set to 0
for correct quaternion multiplications.
B
v =
A
B
ˆq ⊗
A
v ⊗
A
B
ˆq∗ (3.1.6)
For accurate arithmetic operations quaternions need to be normalized first. They can
be easily normalized using equation 3.1.7 [5]
A
B
ˆq = [
q
1
√
q
1
+ q
2
+ q
3
+ q
4
q
2
√
q
1
+ q
2
+ q
3
+ q
4
q
3
√
q
1
+ q
2
+ q
3
+ q
4
q
4
√
q
1
+ q
2
+ q
3
+ q
4
]
(3.1.7)
3.2 Orientation Representation Using Sensor Fusion
To correctly analyze a golf swing the clubs orientation throughout the swing must be esti-
mated. This section describes an algorithm for orientation sensing developed by Sebastian
O.H Madgwick. [20]. It estimates orientation based on integrating gyroscope angular rate
readings. The algorithm increases the reliability of the orientation sensing by using a mag-
netometer and an accelerometer to compensate for gyroscope dirft. Sebastian Magwick
also incorporated a magnetic distortion compensation algorithm for the magnetometer
sensor. The MARG algorithm uses quaternions for orientation representation. Quaternion
notations and operations used in this section are presented in section 3.1.
3.2.1 Orientation from Angular Rate Represented using Quaternion
First we will demonstrate how orientation sensing could be achieved using only a gyro-
scope. Consider a 3-axes gyroscope that measures its angular rate defined as ω
x
,ω
y
and
3. ORIENTATION AND DISPLACEMENT ESTIMATION OF A RIGID OBJECT 29
ω
z
around its respective x , y and z axis . Having the angular rate in radians for each axis
we can construct a quaternion
S
ω:
S
ω = [0 ω
x
ω
y
ω
z
] (3.2.1)
Using the quaternion
S
ω we can compute the rate of change of the earth frame relative to
the sensor frame denoted by
S
E
˙q:
S
E
˙q =
1
2
S
E
ˆq ⊗
S
ω (3.2.2)
Now suppose that we are sampling gyroscope readings
S
ω with sample period of ∆t. If
we are at the n-th sample, then
S
ω
n
will be the gyroscope readying at sample n∆t. Let
us define
S
E
˙q
e,n
to be the orientation of the earth frame relative to the sensor at sample
n. Let us assume that we know the initial orientation
S
E
˙q
e,0
. In that case we can compute
the new compound orientation of the device as shown in 3.2.3.
S
E
˙q
n
=
1
2
S
E
ˆq
e,n−1
⊗
S
ω
n
(3.2.3)
Finally, we can integrate
S
E
˙q
n
to obtain the estimated orientation of the earth frame
S
E
ˆq
e,n
relative to the sensors: [20]
S
E
ˆq
e,n
=
S
E
ˆq
e,n−1
+
S
E
˙q
n
∆t (3.2.4)
The equation above would compute the orientation of an object based only on gyroscope
angular rate. As stated in section 2.2.1, MEMS gyroscope readings drift and they cannot
correct any orientation estimation errors relative to the earth frame. The combination of a
gyroscope with an accelerometer and a magnetometer can compensate for that. Together
the three sensors form a magnetic, angular rate, gravity (MARG) sensor array, [20] such
as the 9 DOF Sensor Stick used in the prototype device.
3. ORIENTATION AND DISPLACEMENT ESTIMATION OF A RIGID OBJECT 30
3.2.2 MARG Sensor Fusion algorithm
The following presentation is an adaptation of the Arduino implementation of the sensor
fusion algorithm by Fabio Verasano. [30] The MARG sensor fusion algorithm estimates
gravity and earth’s flux vectors using an accelerometer and a magnetometer respectively
to compute an adjusted measurement of the gyroscopes angular rate
S
ω. We are going to
call that adjusted angular rate
S
ω
est
.
Consider a 3-axes accelerometer that measures gravitational force a
x
, a
y
and a
z
in its
respective axes. We can construct a quaternion
S
ˆa
n
that contains the gravitational force
measurements at sample n:
S
ˆa
n
= [0 a
x
a
y
a
z
] (3.2.5)
In a similar fashion, we can construct a quaternion that contains a magnetometers’ pro-
jection of the earth’s flux vector at sample n.
S
ˆm
n
= [0 a
x
a
y
a
z
] (3.2.6)
Together, the following quaternions will be the inputs the the MARG sensor fusion algo-
rithm at sample n:
1.
S
ˆa
n
- quaternion containing the raw accelerometer readings in the sensor frame.
2.
S
ˆm
n
- quaternion with magnetometer flux vector in the sensor frame.
3.
S
ˆω
n
- quaternion containing gyroscope angular rate readings in the sensor frame.
The inputs will be used to determine the gravity vector
S
ˆv
n−1
and the estimated direc-
tion of the magnetic field in the sensors frame
S
ˆ
b
n−1
from the previous sample n − 1. We
are concerned with the these vectors because the are used to estimate the difference be-
tween the estimated orientation and the true orientation of the sensor. The output of the
3. ORIENTATION AND DISPLACEMENT ESTIMATION OF A RIGID OBJECT 31
algorithm is quaternion
S
E
q
e,n
that determines the orientation of the earth frame relative
to the sensor.
S
E
q
e,n
is computed as demonstrated in equation 3.2.4 but using the adjusted
angular rate
S
ω
est
n
instead of the unfiltered angular rate
S
ω
n
3.2.3 Algorithm step
If we assume that we have completed step n − 1 of the algorithm then we can compute
the estimated gravity vector
S
ˆv
n−1
as shown in equation 3.2.7. Note that as explained in
equation 3.1.6, if we have a quaternion and its conjugate we can rotate a vector using that
quaternion. That is how the gravity projection vector is computed:
S
ˆv
n−1
=
E
S
ˆq
e,n−1
⊗
E
ˆv ⊗
E
S
ˆq∗
e,n−1
(3.2.7)
If we know the magnetic field vector of the earth
E
ˆ
b we can compute the estimated direction
of the magnetic field in the sensor frame:
S
ˆ
b
n
− 1 =
E
S
ˆq
e,n−1
⊗
E
ˆ
b ⊗
E
S
ˆq∗
e,n−1
(3.2.8)
After that we can compute the error e
n
which is the difference between the estimated
orientation and the true orientation. That is obtained by summing the cross products of
the reference direction of fields and the direction measured by the sensors.
e
n
=
S
a
n
×
S
v
n−1
+
S
m
n
×
S
b
n−1
(3.2.9)
We sum errors from each step by integrating e
n
where k
i
is integral gain for rate of
convergence of gyroscope biases:
S(e
n
) = S(e
n−1
) + e
n
.k
i
(3.2.10)
Finally we compute corrected estimated orientation of the angular rate at sample n,
S
ω
est
n
as follows:
S
ω
est
n
=
S
ω
n
+ e
n
.k
p
+ S(e
n
) (3.2.11)
3. ORIENTATION AND DISPLACEMENT ESTIMATION OF A RIGID OBJECT 32
where k
p
is the proportional gain that governs convergence to accelerometer and magne-
tometer readings. Now that we have the adjusted
S
ω
set
n
angular rate, it will be new input
for our initial algorithm:
S
E
ˆq
e,n
=
S
E
ˆq
e,n−1
+ (
1
2
S
E
ˆq
e,n−1
⊗
S
ω
est
n
).∆t (3.2.12)
3.2.4 Magnetic distortion compensation
As shown in equation 3.2.8 we are assuming that we know the magnetic field vector
E
ˆ
b
that is used to compute error e
n
. However, magnetometer are prone to distortion of nearby
local magnetic fields. Consider that we have measured the direction of the earth’s magnetic
filed at sample n. That direction is denoted by
E
ˆ
h
n
and can be computed as we rotate
the normalized magnetometer measurement
S
ˆm
n
by the orientation estimation quaternion
S
E
ˆq
e,n−1
:
E
ˆ
h
n
= [0 h
x
h
y
h
z
] =
S
E
ˆq
e,n−1
⊗
S
ˆm
n
⊗
S
E
ˆq
e,n−1
(3.2.13)
The effect of the erroneous inclination of the measured direction earth’s magnetic field,
E
ˆ
h
n
, can be corrected if the algorithm’s reference direction of earth’s magnetic field
E
ˆ
b
n
is of the same inclination. That can be achieved by having
E
ˆ
h
n
and
E
ˆ
b
n
normalized to
have only components in the earth frame x and z axes:
E
ˆ
b
n
= [0
q
h
2
x
+ h
2
y
0 h
z
] (3.2.14)
Compensating for magnetic distortions this way ensures that the magnetic disturbances
will only affect the estimated heading component of the orientation. [20]
3. ORIENTATION AND DISPLACEMENT ESTIMATION OF A RIGID OBJECT 33
3.2.5 Algorithm pseudo code
A pseudo code of the MARG sensor fusion is presented in algorithm 1. The algorithm
takes
S
a
n
,
S
m
n
,
S
ω
n
, S(e
n
−1) and the quaternion orientation
S
E
ˆq
e,n−1
from sample n −1
as inputs. The output is the new quaternion orientation of the earth frame relative to the
sensors,
S
E
ˆq
e,n
. Algorithm 2 and Algorithm 3 are pseudo code representation of supporting
methods for the sensor fusion algorithm. Algorithm 2 takes as input the acceleration
reading
S
a
n
and computes the difference in the estimated direction and measured direction
of field vectors. Algorithm 2 filters the magnetometer input
S
m
n
using the methodology
shown in section 3.2.4 and computes the difference in the expected and measured magnetic
direction.
3. ORIENTATION AND DISPLACEMENT ESTIMATION OF A RIGID OBJECT 34
Algorithm 1 AHRS Update
1: Kp {proportional gain constant}
2: Ki {integral gain constant}
Require: Input : g[], a[], m[], q[], integralF B[], deltaT
Ensure: qNew[]
3: e[] {define 3 dimensional array containing the error e
n
}
4: qNew[] {define a new array that is the output of the algorithm}
5: if isValid(m) then
5: { Compute feedback from magnetometer measurements. Method isValid() returns
true if all elements in an array are not equal to 0 }
6: m[] ← normalize(m[]) {normalize magnetometer readings}
7: e[] ← magnetometerError(m[], q[]) { Error is sum of cross product between esti-
mated direction and measured direction of field vectors as shown in equation 3.2.9}
8: end if
9: if isValid(a[]) then
9: { Compute feedback from accelerometer measurements}
10: a[] ← normalize(a[]) {normalize accelerometer readings}
11: e[] ← e[] + accelerometerError(a[], q[])
12: end if
{Apply feedback only when valid error data has been gathered from the accelerometer
or magnetometer }
13: if isValid(e[]) then
13: { Compute and apply integral feedback S(e
n
), where integral error e
n
is scaled by
constant Ki for the three axis as shown in 3.2.10}
14: for i = 0 to 2 do
15: integralF B[i] ← integralFB[i] + Ki ∗ e[i] ∗deltaT
16: end for
17: for i = 0 to 2 do
18: g[i] ← g[i] + integralF B[i] + Kp ∗ e[i] {apply the updated integral feedback and
proportional feedback for the three axis of the gyroscope readings}
19: end for
20: end if
{ Finally integrate rate of change of quaternion as shown in equation 3.2.12}
21: for i = 0 to 2 do
22: g[0] ← g[0] ∗ (0.5f ∗ deltaT ) {pre-multiply common factors }
23: end for
24: qNew[0] ← q[0] + (−q[1] ∗g[0] − q[2] ∗g[1] − q3 ∗g[2])
25: qNew[1] ← q[1] + (−q[0] ∗g[0] − q[2] ∗g[1] − q3 ∗g[2])
26: qNew[2] ← q[2] + (−q[0] ∗g[0] − q[1] ∗g[1] − q3 ∗g[2])
27: qNew[3] ← q[3] + (−q[0] ∗g[0] − q[1] ∗g[1] − q[2] ∗g[2])
28: qNew ← normalize(qNew) {Normalise quaternion}
29: return qN ew
3. ORIENTATION AND DISPLACEMENT ESTIMATION OF A RIGID OBJECT 35
Algorithm 2 accelerometerError
Require: Input : a[], q[]
Ensure: e
v
1: v[] { define 3 dimensional array for the gravity field vector}
{Compute the estimated direction of gravity as shown in 3.2.7 }
2: v[0] ← q[1] ∗q[3] −q[0] ∗ q[2]
3: v[1] ← q[0] ∗q[1] + q[2] ∗ q[3]
4: v[2] ← q[0] ∗q[0] −0.5 + q[3] ∗ q[3]
{The error e
v
is the cross product between estimated direction and measured direction
of field vectors}
5: e
v
[0] ← (a[1] ∗v[2] − a[2] ∗ v[1])
6: e
v
[1] ← (a[2] ∗v[0] − a[0] ∗ v[2])
7: e
v
[2] ← (a[0] ∗v[1] − a[1] ∗ v[0])
8: return e
v
Algorithm 3 magnetometerError
Require: Input : m[], q[]
Ensure: e
b
1: h[] {define the magnetic field vector of the earth}
2: b[] {define reference direction of the earth’s magnetic field}
3: b
s
[] {define estimated direction of the magnetic field in the sensor frame}
{Compute reference direction of Earth’s magnetic field}
4: h[0] ← 2 ∗(m[0] ∗(0.5 −q[2] ∗q[2] −q[3] ∗q[3]) + m[1] ∗(q[1] ∗q[2] −q[0] ∗q[3]) + m[2] ∗
(q[1] ∗ q[3] + q[0] ∗ q[2]))
5: h[1] ← 2 ∗(m[0] ∗(q[1] ∗q[2] + q[0] ∗q[3]) + m[1] ∗(0.5 −q[1] ∗q[1] −q[3] ∗q[3]) + m[2] ∗
(q[2] ∗ q[3] − q[0] ∗ q[1]))
6: b[0] ← sqrt(h[0] ∗h[0] + h[1] ∗h[1])
7: b[2] ← 2 ∗(m[0] ∗(q[1] ∗q[3] −q[0] ∗q[2]) + m[1] ∗(q[2] ∗q[3] + q[0] ∗q[1]) + m[2] ∗(0.5 −
q[1] ∗ q[1] − q[2] ∗ q[2]))
{Compute estimated direction of magnetic field as shown in 3.2.14 }
8: b
s
[0] = b[0] ∗(0.5 − q[2] ∗q[2] − q[3] ∗q[3]) + b[2] ∗ (q[1] ∗q[3] − q[0] ∗ q[2])
9: b
s
[1] = b[0] ∗(q[1] ∗q[2] − q[0] ∗q[3]) + b[2] ∗ (q[0] ∗q[1] + q[2] ∗q[3])
10: b
s
[2] = b[0] ∗(q[0] ∗q[2] + q[1] ∗q[3]) + b[2] ∗ (0.5 − q[1] ∗q[1] − q[2] ∗ q[2])
{Compute cross product between estimated direction and measured direction of field
vectors}
11: e
b
[0] ← (m[1] ∗b
s
[2] −m[2] ∗ b
s
[1])
12: e
b
[1] ← (m[2] ∗b
s
[0] −m[0] ∗ b
s
[2])
13: e
b
[2] ← (m[0] ∗b
s
[1] −m[1] ∗ b
s
[0])
14: return e
b
3. ORIENTATION AND DISPLACEMENT ESTIMATION OF A RIGID OBJECT 36
3.3 Position Estimation
3.3.1 Gravity Compensation
In order to estimate the path of a golf club during a swing, we can use the accelerometer
of the IMU that is attached to the club. The accelerometer will reflect motion of the
IMU system by outputting acceleration at sample n in each of its axes represented by the
last three components of quaternion
S
ˆa
n
. That acceleration has to be integrated twice to
obtain displacement. This method would work correctly only if the device was positioned
so that one of its axes would capture the full force of gravity 1g and that force of 1g is
subtracted from that axis before integration is performed. However, the device will change
orientation during a swing, meaning that the force of gravity 1g will be distributed in
each of the three axes of the accelerometer. That means that the accelerometer’s raw
output is a combination of acceleration due to motion and gravitational force. Therefore,
we need an acceleration vector called
ˆ
d
n
that represents the dynamic acceleration of the
IMU. Dynamic acceleration is only acceleration due to displacement. We know that we
can obtain the expected gravity vector
S
ˆv
n
at the n-th of the sensor fusion algorithm as
demonstrated in equation 3.2.7. We can therefore subtract
S
ˆv
n
from the raw acceleration
readings
S
ˆa
n
, thus getting the expected dynamic acceleration in all three axes of the sensor:
ˆ
d
n
=
S
ˆa −
S
ˆv
n
(3.3.1)
where we can ignore the first element of quaternion
S
ˆa and quaternion
S
ˆv
n
as only their
last three components contain gravitational force estimations.
3.3.2 Displacement Estimation
In order to approximate the position S of the IMU device over time, its speed has to be
calculated. The velocity over time is calculated by integrating the dynamic acceleration
3. ORIENTATION AND DISPLACEMENT ESTIMATION OF A RIGID OBJECT 37
values for each sample n:
v =
Z
n
0
d (3.3.2)
The position of the device therefore would be the result of the integration of the velocity
v:
S =
Z
n
0
v =
Z
n
0
Z
n
0
d (3.3.3)
This method means that acceleration readings must be integrated twice to get displace-
ment. There is a sample time ∆t between consecutive readings. The method described
above is theoretically correct but would not work so well in practice because it requires
very high sampling rate, in order to make ∆t very small. Even when optimized for max-
imum speed the sample rate of the IMU will not exceed 400 Hz. Therefore, to better
estimate the position of the IMU, rectangular midpoint integration will be performed: [18]
ˆv =
Z
n
0
ˆ
d ≈ d
n−1
+ (
d
n
+ d
n−1
2
).∆t (3.3.4)
ˆ
S =
Z
n
0
ˆv ≈ v
n−1
+ (
v
n
+ v
n−1
2
).∆t (3.3.5)
where n is the sample number and ∆t is the time between two consecutive readings.
4
Golf terminology and GolfSwing Application
4.1 Golf Swing phases
Figure 4.1.1: The path of a golf club during a typical full golf swing
[24]
Figure 4.1.1 provides a picture of a golf club during a swing and figure 4.1.2 presents
the composition of a golf club. Small differences in the orientation of the clubface during
impact with a ball will affect the golf ball’s path. In addition, the motion of the club
4. GOLF TERMINOLOGY AND GOLFSWING APPLICATION 39
immediately after impact with the golf ball has a major role in the accuracy of the golf
shot. The whole process that a golf player goes through including body alignment and
preparation is not of key importance for this paper. The motion of the golf club during
a golf swing is the focus of this project as it can be evaluated using the novel hardware
system. That motion can be categorized in four phases: back swing, down swing, contact
and follow-through.
Figure 4.1.2: Composition of a golf club
[27]
The backswing begins as the player moves back the club that is initially placed per-
pendicular to the ground and next to the golf ball. That motion continues in even tempo
until the club is parallel to the ground. The down swing is the next step and it should
repeat the same movement of the back swing, but in opposite direction. The down swing
of course is very fast and can happen in less then half a second. The moment of the impact
of the club face with the ball is called the contact phase. It is a crucial moment, since
that is when the momentum of the club is transferred to the ball. The orientation of the
clubhead and the angle of attack are very important during the contact. The last phase
is the follow-through. During that last phase, the direction of the path of the club can
4. GOLF TERMINOLOGY AND GOLFSWING APPLICATION 40
alter substantially the golf ball’s final location. Note that on average the backswing takes
around 0.8 seconds and the down swing takes 0.3 seconds. [9] That makes for a very short
time frame of recording data using the prototype device. The next subsection elaborates
on the follow through phase and its relevance to a golf player. The phases described above
are used to decide on the way feedback is given to the golf player and the way sensor data
is analyzed.
4.1.1 Follow-through phase
During the follow-through phase, right after the impact with the ball, the club can move
in multiple distinct directions as depicted in figure 4.1.3. That movement can be put in
two major categories: hook and slice. A hook occurs when the clubface follows an inside-
out swingpath and thus flies severely from right to left for a right-handed player. A slice
occurs when the clubface follows an outside-in swingpath and thus flies severely from left
to right for a right-handed player. Skilled players can hook or slice the ball at will, but
most commonly they are misplayed shots. [11]
4. GOLF TERMINOLOGY AND GOLFSWING APPLICATION 41
Figure 4.1.3: Possible paths of the clubhead during the follow-through phase of a golf
swing
[19]
4.2 GolfSwing Application
4.2.1 Processing Application Overview
In this section, we introduces an application called GolfSwing, which interfaces with the
IMU prototype and visualizes a replay of a golf swing. The application can also determine
if a shot was hook or sliced using the follow-through phase data obtained from the IMU.
This is a top-level overview of the application that demonstrates what functions it needs
to perform to be useful for a golf player. I wrote the application using Processing. Pro-
cessing is an open source programming language and environment for people who want
to create images, animations, and interactions. [23] Processing is a good choice for this
application because it supports OpenGL, which is used to graphically represent the mo-
4. GOLF TERMINOLOGY AND GOLFSWING APPLICATION 42
tion and path of the golf club after a golf swing. Figure 4.2.1 shows the interface of the
GolfSwing application used in this project. The user interface was designed with simplicity
and functionality in mind. A user can choose between the following options:
Figure 4.2.1: GolfSwing application and its menu.
1. Record a swing - The attached to a club IMU would start recording data. A second
after its vibration sensor detects impact the IMU will stop recording and notify the
application that it is ready to send the data over bluetooth.
2. Stop recording - Make the IMU stop recording
3. Receive and process data - Ask the IMU for the recording data, receive it and save
it to a CSV file for reference. After that, process the data and save it to another
CSV file containing the clubhead’s position and orientation for each sample.
4. Visualize the golf swing - Visualize the motion of the golf swing with chosen replay
speed using OpenGL API
4. GOLF TERMINOLOGY AND GOLFSWING APPLICATION 43
5. Show club’s path - Shows the whole path of the clubhead and the IMU by connecting
the points representing their locations for each sample.
6. Graphically inspect sensor values for data analysis - Show the acceleration and ve-
locity change over time on a graph for data analysis.
7. Construct feedback - determine if the shot hooked or sliced.
4.2.2 Feedback on a golf swing
In order to give constructive feedback, the golf swing application use the concepts of
hook and slice. To determine the specific hook or slice, the change in orientation and
displacement following the impact with the ball are checked. It is sufficient to trace the
change in the x and y position of the clubhead for half a second after the impact with
the ball. Thus the amount of movement of the club sideways results in a feedback score
in the range from 1 to 10, where 1 would indicate a straight shot and 10 would indicate
a maximum slice or hook movement. Figure 4.1.3 shows some of the possible movements
of the club after impact. Using the latter technique, each of these movements could be
approximated. In addition, the GolfSwing application can calculate the velocity of the
club at the moment of impact and the maximum velocity, throughout the whole swing.
4.3 IMU System Data Recording Process Overview
Once the IMU microcontroller is notified to start recording it gets the raw readings from
the accelerometer, gyroscope and magnetometer. Then it performs the sensor fusion al-
gorithm on the readings. I adapted a library called FreeIMU that implements the sensor
fusion algorithm for Arduino [31]. I modified it to work with 32-bit micro controllers in-
cluding Teensy 3.0, by optimizing its drivers for the sensors. In addition to that I added
gravity compensation to the accelerometer’s raw readings to extract dynamic acceleration.
4. GOLF TERMINOLOGY AND GOLFSWING APPLICATION 44
While recording, the microcontroller saves on the MicroSD Card the following: a quater-
nion array q, dynamic acceleration array d and sampling time float t for each sample. Once
the IMU system stops recording it reads the data from the saved file on the MicroSD card
and sends to a processing application over bluetooth. The average size of that data is 32
bites. The average sample rate of the configuration when data is logged is 400 Hz. If the
data is not saved on the MicroSD card the sample rate is 900 Hz.
5
Sensor Performance Optimization and Data
Processing Algorithm
This chapter contains a discussion of the performance of the IMU system’s individual
sensors. The output of the MARG sensor fusion algorithm, discussed in section 3.2.2, is
processed with several techniques to achieve optimum results in a golf swing trajectory
prediction. We also investigate the prototype’s most fit attachment location on a golf
club. Each component of the IMU system is inspected and improved independently in
order to construct an algorithm suitable for orientation and displacement estimation of a
golf clubface during a swing. Note that we assume that in any case the device will not
record data for more than 20 seconds. After all, the process of backswing and downswing
takes less than 2 seconds on average. [9]
5.1 Orientation and displacement estimation without filters
Our final sensor fusion algorithm returns the IMU’s quaternion orientation estimation -
S
E
ˆq
e,n
, dynamic acceleration vector
ˆ
d
n
and time step ∆t between sample n and n − 1. It
is important to investigate the accuracy of that data independently, so that any of its
components that are prone to errors can be optimized using filtering.
5. SENSOR PERFORMANCE OPTIMIZATION AND DATA PROCESSING ALGORITHM46
5.1.1 Orientation estimation without filtering
To evaluate the orientation estimation capabilities of the IMU, I kept it stationary for 20
seconds and observed its Euler angles estimation over time.
Figure 5.1.1: Determining the orientation of the device and displaying it using Processing
Figure 5.1.2 shows the drift of the estimated roll , pitch and yaw angles of the IMU for
20 seconds. As depicted in the graph, the drift accumulates to no more than 5 degrees. The
IMU system’s orientation is very stable mainly because it is obtained using the MARG
sensor fusion algorithm shown in section 3.2.2 and because the device has 9 degrees of
freedom. The addition of a magnetometer is essential, since with the magnetometer out-
put, the IMU system can sense its orientation in reference to the earth’s frame. If no
magnetometer were present the IMU would not be able to correct its yaw estimation.
5. SENSOR PERFORMANCE OPTIMIZATION AND DATA PROCESSING ALGORITHM47
Figure 5.1.2: Yaw Pitch Roll estimations when IMU is placed stationary
So far the IMU system indicates successful orientation capabilities for our needs. How-
ever, in order to record a golf swing, the device that is attached to a club has to change
orientation rapidly. Evaluation of its orientation sensing accuracy during rotational mo-
tion is demonstrated below. The IMU is placed on an actuator that can rotate its axle any
chosen angle. (Figure 5.1.3) The point of the experiment is to compare the approximated
orientation to the actual orientation of the device over the course of several axle rotations.
The actuator axle repeats the following process over time: turn clockwise 180 degrees,
instantly change direction and turn counter clock wise 180 degrees, delay for roughly a 0.8
seconds and repeat the process.
5. SENSOR PERFORMANCE OPTIMIZATION AND DATA PROCESSING ALGORITHM48
Figure 5.1.3: Actuator setup used to rotate the IMU
By rotating the IMU we can evaluate its orientation sensing accuracy
Figure 5.1.4 shows the result of that experiment. The figure reflects the axle rotation
process and also demonstrates that the device has good orientation estimation capabilities
in a dynamic setting. After 8 consecutive turns, the IMU still has accurate estimation of
its initial heading and attitude at the beginning of the experiment.
5. SENSOR PERFORMANCE OPTIMIZATION AND DATA PROCESSING ALGORITHM49
Figure 5.1.4: Euler angles estimation during actuator rotation
The successful orientation estimation of the IMU system over time implies that at
the moment of impact with a golf ball the device can theoretically sense the club face’s
orientation with minimal error if it has been recording data for less than 20 seconds. We
can safely assume that the orientation sensing process does not need filtering because the
angular velocity is only integrated once and because in its current configuration the IMU
is capable of very effective orientation estimation.
5.1.2 Position estimation without filtering
Ideally, the displacement of the IMU would be the result of integrating twice the compo-
nents of the dynamic acceleration vector
ˆ
d as shown in section 3.3.2. However, there is a
potential problem with employing only that technique. When double integrating constant
acceleration, errors increases with the square of time because the error after 20 seconds
is 400 times greater than that at 1 second. Any small offset errors in the acceleration
measurement will quickly produce an intolerable error level. [3] In addition to that, all
5. SENSOR PERFORMANCE OPTIMIZATION AND DATA PROCESSING ALGORITHM50
position estimation are based entirely on the dynamic acceleration output
ˆ
d. The process
of acquiring dynamic acceleration described in Section 3.3 can lead to additional errors
because any difference in the IMU’s orientation estimation and its real orientation will
lead to inaccurate estimation of the gravity vector
S
ˆv
n
. Since the components of the grav-
ity vector are removed from the accelerometer output vector
S
ˆa
n
, if the gravity vector
estimation is not fully accurate, error will accumulate.
Finally, figure 5.1.5 depicts the expected position of the device based on double midpoint
rectangular integration when the IMU prototype is placed stationary on a flat surface.
Figure 5.1.5 shows that after only 6 seconds the expected displacement of the system in
just its x axis is more than 30 meters.
Figure 5.1.5: IMU’s displacement over time without any filtering
It is clear that non filtered data would not be reliable over a time frame of more than a
few seconds. Demonstrating the displacement estimation of the system when it undergoes
motion is unnecessary because the error is increasing so rapidly even when it is not mov-
5. SENSOR PERFORMANCE OPTIMIZATION AND DATA PROCESSING ALGORITHM51
ing. A filtering technique must be applied to the process of double integrating dynamic
acceleration. The next section proposes a methodology for that purpose.
5.2 Displacement estimation optimization
It is necessary to filter the dynamic acceleration output even though that can lead to
less precise displacement calculations. Filtering reduces the risk of calculating a position
estimation that is completely inaccurate compared to the actual position of the device. In
other words, it is better to estimate displacement that contains the general motion of the
IMU’s physical movement versus displacement estimation that becomes useless after less
than a second. Therefore, we propose a methodology for processing dynamic acceleration
vector
ˆ
d for each sample from 0 to n.
1. Having input
ˆ
d
n
, we want to compute position vector ˆs
n
and velocity vector ˆv
n
. For
a given dynamic acceleration
ˆ
d
n
, we first check if the absolute value of any of the
elements of the vector are below a threshold. That threshold is 0.1g. If any of the
components
ˆ
d
x
n
,
ˆ
d
y
n
or
ˆ
d
z
n
of the vector
ˆ
d
n
have a gravitational force measurement
whose absolute value is below the threshold, we set that component to 0. We do that
because we want to filter erroneous acceleration output.
2. Integrate
ˆ
d
n
to obtain velocity. We then check if the absolute value of the acceleration
from the previous 10 samples of dynamic acceleration
ˆ
d are below the threshold 0.1g.
If that is the case than we set the value in the axis of the velocity vector ˆv to 0. We
do this because we assume that the device is stationary and that it is not changing
direction. We do not want to integrate velocity ˆv
n
when the device is not moving
because position estimation would quickly produce intolerable error.
3. Finally we integrate the velocity to get position ˆs
n
at sample n.
5. SENSOR PERFORMANCE OPTIMIZATION AND DATA PROCESSING ALGORITHM52
Figure 5.2.1 shows the x, y and z displacement estimation with the filtering techniques
described above when the IMU is placed stationary on a flat surface. Ideally over 6 seconds
displacement in each axis should be 0. That is precisely the case as figure 5.2.1 demon-
strates. Since we are resetting the acceleration whenever it bellow 0.1 g any error is filtered
before any integration is performed. It is safe to have a threshold of 0.1 g as during golf
swing the acceleration of the golf club is well above 5g, meaning that we will not reset
acceleration due to the actual club’s displacement.
Figure 5.2.1: IMU’s displacement over time with filtering
5.3 IMU Placement on a Golf Club
The IMU prototype has to be physically attached to a golf club to record data during
the swing. The average length of a golf club is 40 inches [12] meaning that there are
multiple locations where the device can be attached. In this section, two possible placement
locations for the IMU system are examined : the golf club’s grip area at the top and the
club head’s area at the bottom. The two different locations of the IMU would involve two
different procedures for displacement estimation of the club head.
5. SENSOR PERFORMANCE OPTIMIZATION AND DATA PROCESSING ALGORITHM53
5.3.1 IMU at the head of the club
If the IMU system is placed at the bottom of the golf club, the clubhead’s position estima-
tion will depend entirely on the double integration of acceleration values. In addition to
that, even a prototype of small size and weight would negatively impact the performance
of the golf swing, as it adds extra weight to the clubhead. Golf clubs are tuned for a specific
weight distribution and even a small addition of mass at the end of the club will alter the
desired flight of the ball. For these reasons reasons, having the IMU at the bottom of golf
club is not a desirable option.
5.3.2 IMU at the grip of a club
The IMU can easily be attached right below the grip of a golf club. The length of a golf
club grip is roughly 0.25 meters therefore the IMU would be placed at 0.3 meters from the
top of the club. Placed at that distance, it will not affect the club’s weight distribution
as much as it would at the the club head. Having the IMU near the grip means that the
position estimation of the club head will be a combination of the double integration of
acceleration data and a projection of the club shaft based on the IMU’s orientation.
5.4 Final Displacement and Orientation Estimation Processing
Algorithm
This section presents an overview of the process of estimating the position and orientation
of a golf club head with the IMU system attached below the club’s grip. Consider that
the IMU is attached on a golf club below the club’s grip. In that case the distance from
the IMU’s accelerometer sensor to the club head would be denoted by k. The length of
the club itself is 1 meter. The cartesian vector denoted by
ˆ
S is the vector containing the
final x, y and z coordinates of the clubhead in three-dimensional space.
5. SENSOR PERFORMANCE OPTIMIZATION AND DATA PROCESSING ALGORITHM54
Since the IMU system is placed below the grip, its orientation will be used to estimate
the three-dimensional coordinates of the clubhead that is at distance k from the IMU’s
accelerometer. As described in 3.1.6, we can rotate a vector of certain length using a
quaternion. Lets construct such a vector ˆp
in
of length k.
ˆp
in
= (0, 0, 0, −k) (5.4.1)
In this case having −k as the last component of ˆp
in
means that the the projection of the
clubhead would be an extension of the z axis of the device. The vector ˆp
out
is vector ˆp
in
of a length k, rotated using normalized quaternion ˆq. Quaternion
ˆ
q∗ is the conjugate of ˆq.
The first element of the two 4 dimensional vectors ˆp
out
and ˆp
in
is 0.
ˆp
out
= ˆq ⊗ ˆp
in
⊗
ˆ
q∗ (5.4.2)
The vector ˆp
out
will contains the coordinates of the end of the club if it rotates around a
fixed point and if the accelerometer of the IMU system is placed on that fixed point. Since
the IMU must be placed on the grip the final location of the clubhead
ˆ
S is the sum of the
vector ˆp
out
and the vector containing the coordinates of the IMU’s accelerometer.
The final heading and displacement algorithm returns the clubface’s estimated orienta-
tion
S
E
ˆq
e,t
and position
ˆ
S. We simply sum the vector containing the Cartesian coordinates
of the IMU’s accelerometer ˆs
imu
with the vector containing the coordinates of the club
head’s expected position ˆp
out
to obtain the final position vector
ˆ
S:
ˆ
S
n
= ˆs
imu
+ ˆp
out
(5.4.3)
The vector
ˆ
S
n
represents the final location of the clubhead in 3D space for each sample
n. Its coordinates are saved in a designated data structure using the GolfSwing Processing
application and thus the golf swing can be visualized.
6
IMU Prototype Evaluation with Simulations
6.1 Process of Evaluation
In order to evaluate the IMUs performance, an environment with proper golf swing sim-
ulation equipment for conducting tests is essential. The output of the final displacement
algorithm in section 5.4 has to be empirically compared to its expected true result. We
need to be able to put the device through approximately the same type of motion and ori-
entation change, multiple times. In addition to that, the position of the IMU at any given
time must to be known. The system’s performance and other technical and economical
aspects are evaluated in this chapter.
6.2 Golf Swing simulation using Pendulum
The IMU’s golf swing recording and analyzing capabilities have to be considered and
evaluated. A pendulum is an excellent candidate for golf swing simulations and empirical
evaluation. A pendulum is a weight suspended from a pivot so that it can swing freely.
When a pendulum is displaced sideways from its resting equilibrium position, it is subject
to a restoring force due to gravity that will accelerate it back toward the equilibrium
6. IMU PROTOTYPE EVALUATION WITH SIMULATIONS 56
position. When released, the restoring force combined with the pendulum’s mass causes
it to oscillate about the equilibrium position, swinging back and forth. [22]
6.2.1 Nonlinear Driven Damped Pendulum
Pendulums are most often modeled with a a string and a mass at its end, making the
force of friction and air resistance negligible. A string cannot accommodate the needs
of this experiment because the IMU must be attached on a rigid rod. Using a rigid rod
means that friction cannot be neglected. That means that the pendulum is underdamped.
[10] A model for such a damped pendulum is presented here. The angular frequency of
the damped pendulum is Ω. The frequency can be calculated using the period T of a
pendulum:
Ω =
1
T
(6.2.1)
where T is in seconds and Ω is in sec
−1
. Equation 6.2.2 shows how to compute the
expected angle θ of the rod over time. [10]
θ = θ
0
e
−t/γ
cos(Ωt) (6.2.2)
where the initial angle θ
0
and the expected angle θ are in radians and γ is the expected
decay time. The constant γ depends on friction of the rod and air resistance but for our
needs we can assume it is 0.5. [10] Finally we can compute the expected x and y position
of a pendulum rod of length L given the rods angle θ:
x = L sin(θ) (6.2.3)
y = L cos(θ) (6.2.4)
6. IMU PROTOTYPE EVALUATION WITH SIMULATIONS 57
A pendulum rod follows a circular trajectory. Nevertheless a pendulum is sufficient to
effectively test the performance of the prototype IMU as the goal is to compare the output
of the displacement and position estimation algorithm to some true data.
6.3 Simulation Pendulum Environment
I constructed a pendulum equipment that can be used to perform the same experiments
multiple times. The pendulum’s rod is made of wood and its length is 1 meter. The
simulation involves releasing the pendulum rod at an angle θ of 90 degrees. That is a
suitable release angle because we will simulate the down swing, the contact and the follow
through phase of a golf swing. To ensure that during testing the IMU will be released at
an angle of precisely 90 degrees I placed a metal piece positioned so that I can release the
rod at exactly 90 degrees. The IMU system is attached so that the accelerometer sensor
is at a distance of 30 cm from the rotation axle. That means that the IMU is below the
grip of the club. Figure 6.3.1 shows the pendulum with the IMU attached at an angle of
90 degrees. Using a stopwatch, I timed the pendulum’s period 20 consecutive times after I
released it at an angle of 90 degrees. The average period of the pendulum was 1.86 seconds
and that is the period based on which the pendulum rod’s expected angle over time was
computed using equation 6.2.2.
6. IMU PROTOTYPE EVALUATION WITH SIMULATIONS 58
Figure 6.3.1: Pendulum equipment designed to simulate a simple golf swing
6.4 Experiment’s Results
The golf swing simulation using the pendulum equipment was performed 40 times to ob-
serve the consistency of the accuracy of the IMU device. For each simulation the accuracy
in each axis, and the path and position over time of the club in three-dimensional space
was recorded. Data analysis was performed using a modified version of the GolfSwing
application. A simulated pendulum object was created using the application. To measure
the accuracy of a particular simulations we are comparing the coordinates of the vectors
representing the end of the objects rod’s position over time and the projected club head’s
position over time. Figure 6.4.1 through figure 6.4.4 depict histograms of the average accu-
racy in each axis for the 40 golf swing simulations that were conducted in the methodology
described in section 6.3
6. IMU PROTOTYPE EVALUATION WITH SIMULATIONS 61
Figure 6.4.5: The accuracy for 40 golf swing simulations for 0.93 seconds.
The mean accuracy of all simulations is 80%. To inspect the performance of the club head
position estimation algorithm in more depth we are taking a look at a swing simulation
with average accuracy of 79%. Figure 6.4.6 shows the path of the pendulum versus the path
of the club over the time of 0.93 seconds as that is half the period of the pendulum. For
half a period, the physical pendulum simulates a down-swing and follow-through motion
as in a real golf swing.
6. IMU PROTOTYPE EVALUATION WITH SIMULATIONS 63
Figure 6.4.7: The path of the clubhead and the end of the pendulum rod of a simulation
Finally it is worth examining the IMU’s displacements estimation capabilities over a
period of more then a second. Figure 6.4.8 depicts the three-dimensional path of the
clubhead and the pendulums path over 5 seconds.
6. IMU PROTOTYPE EVALUATION WITH SIMULATIONS 65
contribute to reducing the magnitude of displacement when the IMU undergoes fast motion
and experiences gravitational force that is higher than 0.1g.
The IMU’s clubhead projection based on the device’s orientation seems to play a major
role in representing the club head’s path as shown in figure 6.4.6. It is important to note
that as figure 6.4.8 shows, the path estimation of the clubhead for 5 seconds is fairly
consistent. Although the pendulum’s rod swings back and forward multiple times and
the acceleration experienced by the accelerometer’s axes changes drastically the estimated
path of the clubhead is fairly accurate. That implies that in its current configuration the
device could be used as an inertial navigation system, but some more advanced filtering
methods should be applied to the accelerometers data to compensate for the sample rate
of 400 Hz. Kalman filter is one such technique.
6.5.2 Other evaluation aspects
In this section, we include other factors involved in determining how well the IMU performs
and its de facto practicality. Most of them come from the goal of the project outlined in
Chapter 1. Its total cost is $197 and it is constructed entirely using commercially available
products. That means that it can be assembled and used for inertial navigation purposes
or other applications. On the technical side, the number of degrees of freedom, size ,
weights and robustness are other important evaluation factors. The IMU has 9 DOF and
is protected by a removable enclosure. It has Bluetooth capabilities which are nowadays
standard for any computer or mobile device. That makes facilitating communication easy.
Although the IMU is a prototype it is very small and light. Powered by battery it can
work for more than 2 hours.
A company called Xsens produces motion and orientation tracking sensors used in sev-
eral industries. Figure 6.5.1 provides a comparison between the technical characteristics
of our prototype IMU and the company’s entry level model MTi 10-series. [33]
6. IMU PROTOTYPE EVALUATION WITH SIMULATIONS 66
IMU prototype Xsense IMU
Price $197 $ $1,290
Degrees of freedom 9 DOF 6 DOF
Feature Vibration Sensor, SD card adapter
Communication Bluetooth, USB RS422 Interface
Accelerometer 16g 5g
Gyroscope 2000 deg/sec 450 deg/sec
Size 101x50x25 mm 57x42x23 mm
Sample Rate 400 Hz 400 Hz
Table 6.5.1: A comparison between the prototype IMU and the Xsense entry level model
IMU
Although the device is just a prototype and does not come with the sophisticated soft-
ware support offered from an established company, it is nevertheless significantly cheaper
and easier to modify. It even has better technical specifications the the Xsense IMU. Over-
all the IMU prototype is a robust configuration, that can deliver performance especially
if it’s sensors output is processed according the specific use of the device.
7
Conclusion and Future Work
The goal of this project was to design and evaluate a hardware system that can be attached
to a golf club and used to analyze a golf swing and its key parameters. A software that
can interface the hardware system was created to visualize a golf swing trajectory and
potentially give feedback to a golf player. The prototype system is easy to built and
significantly cheaper compared to other products with similar characteristics. Its price of
only $197 and the modularity of its components make it a great hardware for research
involving inertial navigation and orientation sensing. We demonstrated that the prototype
has excellent accuracy for attitude and heading estimation. The trajectory of a simulated
golf swing was calculated with an average accuracy of 80%. Such accuracy is sufficient to
determine if a golf swing is hooked or sliced, which is something that a golfer would like
to know without the use of high speed cameras or a golf instructor.
The development and improvement of the IMU device can be continued as follows. The
system can be evaluated using a more sophisticated equipment that can simulate a variety
of golf swings including hooked or sliced shots. A faster data logging methodology for
the IMU’s output samples can be considered as that will significantly increase the sample
7. CONCLUSION AND FUTURE WORK 68
rate of the configuration. Finally a more complex filtering method could be applied to the
dynamic acceleration used to estimate displacement.
MEMS sensors would only become smaller and more efficient in the future as tethnology
advances. Devices like the IMU proposed in this paper can become popular in many aspects
of life. The system can be potentially used in other sports such as baseball or tennis. It
can also be used in other industries since it can log large amounts of data and observe
orientation change and displacement patterns.
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